Title page for ETD etd-03142009-040740
|Type of Document
||Kreider, Marc Alan
||A numerical investigation of the global stability of ship roll :invariant manifolds, Melnikov's method, and transient basins
||Master of Science
|Nayfeh, Ali H.
|Hendricks, Scott L.
|Mook, Dean T.
|Date of Defense
A parametrically forced, single-degree-of-freedom equation modelling ship roll is investigated
through the numerical study of invariant manifolds, Me1nikov's method, and transient basins. The
calculation of the manifolds is facilitated through the development of a sophisticated algorithm for
approximating the locations of the saddle points of the Poincaré map. For selected fixed values
of the restoring-moment and damping parameters (the "base case"), the manifolds of the saddles
of the Poincaré map are repeatedly computed for increasingly higher excitation amplitudes until
homo clinic , heteroclinic, and mixed manifold intersections are observed. The critical amplitudes
at which these tangles first occur are accurately predicted by Melnikov's method, verifying its
viability as a tool for analyzing ship roll. Corresponding transient basins indicate that fractally
mixed regions of stable and unstable initial conditions appear with the onset of transverse manifold
intersections. For parametric forcing, the fractal areas are symmetric about the origin and do not
significantly affect the integrity of the safe region near the origin. Test cases involving external or
combined external-plus-parametric excitation result in asymmetric transient basins and, following
the appearance of manifold tangling, a catastrophic reduction of the safe area. Lastly, Melnikov's
method is used to perform a parameter study that indicates the effects of varying the
restoring-moment and damping coefficients on the critical excitation level.
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